Fast Weighted Universal Transform Coding: Toward Optimal, Low Complexity Bases for Image Compression

In 1], EEros and Chou introduce a two-stage universal transform code called the weighted universal transform code (WUTC). By replacing JPEG's single, non-optimal transform code with a collection of optimal transform codes, the WUTC achieves signiicant performance gains over JPEG. The computational and storage costs of that performance gain are eeectively the computation and storage required to operate and store a collection of transform codes rather than a single transform code. We here consider two complexity-and storage-constrained variations of the WUTC. The complexity and storage of the algorithm are controlled by constraining the order of the bases. In the rst algorithm, called a fast WUTC (FWUTC), complexity is controlled by controlling the maximum order of each transform. On a sequence of combined text and gray-scale images, the FWUTC achieves performance comparable to the WUTC at 1/32 the complexity for rates up to about 0.10 bits per pixel (bpp), 1/16 the complexity for rates up to about 0.15 bpp, 1/8 the complexity for rates up to about 0.20 bpp, and 1/4 the complexity for rates up to about 0.40 bpp. In the second algorithm, called a jointly optimized fast WUTC (JWUTC), the complexity is controlled by controlling the average order of the transforms. On the same data set and for the same complexity, the performance of the JWUTC always exceeds the performance of the FWUTC. On the data set considered, the performance of the JWUTC is, at each rate, virtually indistinguishable from that of the WUTC at 1/8 the complexity. The JWUTC and FWUTC algorithm are interesting both for their complexity and storage savings in data compression and for the insights that they lend into the choice of appropriate xed-and variable-order bases for image representation.